Experimental testing of Risk Aversion

Experimental testing of risk-aversion has been widespread, but at the same time, rather inconclusive. Experiments ranging from field experiments with farmers in India and high-payoff experiments in China, to experiments testing rats' preferences over cups of water at Texas A & M have not really shed much light on how to appropriately model risk-aversion. At the same time, they have led to some interesting insights regarding both human and rat behavior in the presence of uncertainty.

Payoff and Incentive Effects

Binswanger (1980) conducted a field experiment with 330 farmers in rural India. The games were played 7 or 8 times over 6 weeks, with a coin toss determining the outcome, and had payoffs that were fairly high relative to the farmers' incomes. Subjects were asked to choose between lotteries in a manner similar to that used by Allais, but the riskier alternatives were a mean-preserving spread of the less risky ones - they had the same expected value, but a higher variance of payoffs.

For example, in one case, farmers could choose between B, a lottery offering Rs. 40 and Rs. 120 with 50% probability each, and B*, a lottery offering Rs. 35 and Rs. 125 with 50% probability each.

When payoffs were small, about half the respondents were in the intermediate and moderate risk-aversion categories. Nearly a third were close to risk-neutral or risk-loving, and less than 10% were severely risk-averse. However, as payoffs rose, nearly 80% of the subjects displayed moderate risk-aversion, and risk-neutral or risk-loving behavior almost disappeared. Arrow's prediction held - absolute risk-aversion declined as payoff increased, i.e. an individual's willingness to accept small bets of a fixed size increased as wealth increased. However, contrary to Arrow's hypothesis, the subjects also displayed decreasing relative risk-aversion.

Kachelmeier and Shehata (1992) conducted a series of laboratory experiments in China, to elicit people's certainty equivalents for a sequence of lotteries. Once again, conducting the experiments in a developing country allowed the experimenters to have very large payoffs, relative to the subjects' income. Ten session were conducted with 185 student volunteers at Beijing University. The study differed from Binswanger's in that here, subjects were not asked to choose between lotteries. Rather, certainty equivalents were elicited for individual lotteries. Several win percentages were used, not just the uniform 50-50% chances that Binswanger used. Sessions with 77 and 80 subjects each were also conducted in Canada and the U.S. respectively.

Subjects were presented with a lottery involving a prize of value G with probability p, and zero with probability (1-p). They were asked to write their minimum acceptable selling price for this lottery. Then, a deck of 100 cards with amounts ranging from G/100 to G, in increments of G/100 was shuffled, and each subject drew a card. If the value on the card was greater than or equal to the subject's minimum selling value, they were awarded that amount. Otherwise, they played the lottery. (The lottery itself also used a deck of 100 cards, with cards numbered from 1 to 100. If the subject drew a card with a number less than or equal to p, they were awarded the prize.) The value of p was varied between 5% and 95%, in no discernable order.

They found that the average ratios of certainty equvalents to expected values for the high-prize trials were systematically lower than the ratios for low-prize trials, across win percentages. Once again, there was a marked trend from risk-loving or risk neutral preferences to risk-averse, as payoffs increased.

There was also a strong trend observed with reference to win probabilities. However, it did not follow the pattern predicted by prospect theory - that risk aversion should increase at high win probabilities. This may be a result of differences between willingness-to-pay and willingness-to-accept measures, according to the authors. Subjects tend to put a high selling price on something they “own” and a lower buying price on something they do not. At the same time, wealth effects were not found to be significant.

Holt and Laury (2002) used a menu of paired lottery choices, similar to Binswanger, but they included some rounds where the choices were hypothetical. The crossover point to the high-risk lottery was used to infer the degree of risk-aversion. The payoffs for Option A, $2.00 or $1.60, were less variable than the potential payoffs of $3.85 or $0.10 in the "risky" option B. The probabilites were explained using throws of a ten-sided die, and ranged between 1/10 and 10/10, i.e. a sure win.

To control for wealth effects between the high and low real-payoff treatments, subjects were required to give up what they had earned in the first low-payoff task in order to participate in the high-payoff decision. To check the effects of high payoffs, each of the possible payoffs was multiplied by a factor of 20, 50, or 90. In the two "50x" sessions (19 subjects), the “safe” payoffs were $100 and $80, while the “risky” payoffs were $192.50 and $5. In the "90x" sessions (18 subjects) the safe and risky payoffs were ($180, $144) and ($346.50, $9), respectively.

Most subjects chose the safe option when the probability of the high payoff was small, and then "crosssed over" to option B, almost never returning to A. A few more returned in the hypothetical treatment. Once again, the subjects showed increasing degrees of risk-aversion in the high-payoff treatments than the low-payoff treatments. However, this effect was not observed in the hypothetical treatments, casting doubts on the validity of using hypothetical questionnaires to elicit preferences regarding high stakes.

A post-experiment questionnaire was distributed to collect information about demographics and academic background. The subject pool showed a wide variation in income and education, and some interesting patterns appeared. Using the any of the real-payoff decisions to measure risk aversion, income had a mildly negative effect on risk aversion. Other variables (major, MBA, faculty, age, etc.) were not significant. Using the low-payoff decisions only, they found that men were slightly less risk averse than women, making about 0.5 fewer safe choices. Surprisingly, the gender effect disappeared in the high-payoff treatments. The race variable was also not significant.

The effect of institutions

Isaac and James (2000) used a first-price auction in order to arrive at numerical estimates of implied risk parameters. Their procedure was as follows:

First, each subject bidded against 4 computerized bidders in a first-price auction for 40 rounds.

After that, subjects sold a lottery with a 50% chance of winning 0 and a 50% chance of winning $4, according to the Becker-DeGroot-Marschak mechanism (1963). This has a theoretical dominant strategy for participants to reveal their true homegrown value for an item. This procedure aims to elicit subjects’ certainty equivalents for lotteries by means of a demand-revealing mechanism, i.e. the second price auction applied to a lottery. Specifically, a subject owns a lottery. The subject submits a selling price for this to the experimenter in the knowledge that a random number generator will emit a number. The higher of the random number and the seller’s stated value is awarded the right to the eventual proceeds of the lottery. If the right to the lottery proceeds does change hands, the transaction occurs at the higher of the two numbers.

Most, but not all, of the subjects were more risk-seeking in the second-stage procedure. Interestingly, individuals whose bids in the first-price auction were relatively risk-neutral chose actions in the second stage that remained relatively risk neutral, and those individuals whose bids in the first price auction were relatively risk-averse tended to become relatively risk-loving in the second stage.

Rats

Battalio, Kagel, and MacDonald (1985) conducted a series of experiments on many areas of consumer theory, including risk-aversion, using rats as subjects.

In the first experiment, rats had to choose over prospects with equal expected values and mean-preserving spreads. Risk-aversion over food pellets was satisfied throughout.

The second experiment looked at risk-aversion over consumption measured by the daily food intake, which was varied by up to 200%. The low-consumption levels were insufficient for the rats' nutritional requirements and led to rapid weight loss; the high-comsumption levels approached satiation. The rats displayed mildly decreasing risk-aversion, with no tendency towards risk-loving behavior.